I line my sights up on the target (for this example I'm firing at a paper target).

The shot if fired and the bullet hits the target very close to where I was aiming.

After firing the shot my rifle seems to move up in the air and then when it settled down my sights are now pointing left and below where I was originally pointing! About three inches left and five inches below.

I learnt to shoot in the military (reserves) and I'm sure we were told that if you were holding the rifle in the correct position then when you fire a shot, the rifle would rise after you fire and then return to the very same aim point after.

As I'm not doing this it is either me holding the weapon incorrectly, or something else.

Um, I'm not sure I have a good answer. Returning to POA I always understood as just a matter of practice. Certainly holding the rifle correctly is a requirement but not in itself going to make this happen. Sounds like overcompensation but I don't consider myself an expert on this. If you used to a larger caliber rifle and switching to a 22 certainly could see this response happening. I was wondering about the suppressor because depending on the construction a dirty one can cause crazy behavior.

Are you maintaining the same spot-well (cheek on stock)? If you are not, your POA will vary every shot. You must maintain the same spot-well with every shot or you'll be all over the target "left, right, top, and/or bottom". You could also have running sights. Whereas, the adjustment slides as you shoot, thus changing the POI. Check the scope dials and/or the fixed sights to ensure all is tight with no movements during shooting....
Hope this helps some,
kcbuck

If your shots through the scope are staying zeroed and accurate, your problem isn't with the suppressor or the scope. If your rifle isn't coming close to being lined back up on the target after recoil, the problem is with your shooting - either your grip/stance or cheek weld or something.

Try aiming at the target, then keeping your eyes closed, kind of shrug your shoulders and roll your neck a little and bring the rifle back to a normal, firm grip and cheek weld. This is your natural point of aim. Then open your eyes. If you are off-target make adjustments with your middle and lower body until you are back on target (your feet if you're standing, your waist if you're sitting) - this should align your natural point of aim with the target.

If the after shooting this way your rifle comes to rest still way off target after recoil, the problem is likely that you are fighting the recoil - just relax and go with it.

If none of this works, fly town to Texas and visit KC - I hear his whole family are crack-shots with .22's